#### FractalAudio

Fractal Audio Systems
Moderator
The decibel is a unit of measurement that gives the ratio of the power of one signal relative to another. The formula for the decibel is dB = 10 * log_10(P1 / P2) where P1 and P2 are power measurements. The reason it is called a decibel is because it is 10 bels. One bel would be log_10(P1/P2).

The important thing to understand is that the decibel is a RATIO of powers. A dB is meaningless without a reference power. So if someone says "that signal is 86 dB" that is a meaningless number as it has no reference.

Decibels are convenient because they convert logarithmic perception to a linear scale. Human hearing, for example, is logarithmic. Many other natural phenomena are logarithmic which means that the phenomena exists in the "multiplication domain" as opposed to the "addition domain". For example, human vision is logarithmic. We perceive light such that the light must double for it to appear twice as bright. If we were to plot that we would have an exponential curve of light intensity vs. perceived brightness. If we take the logarithm of the intensity instead we get a straight line. This is why cameras use f-stops which are a base-2 logarithm.

So, back to reference levels. There are many reference levels used in dB: dBm, dBu, dBV, dB re. kPa, etc. dBm refers to the power referenced to one milliwatt. If the measured power is, say, 100 mW then that would be 10 * log10(100/1) = 10 * log10(100) = 20 dBm. dBV is a voltage ratio and not really a true dB but, regardless, is still commonly used. The formula for dBV is 20 * log10(V1/V2) since we need to square the voltage to get the power.

In audio a common unit is dBu. dBu is the power relative to the voltage into a 600 ohm resistor that is dissipating 1 mW. This is roughly 0.77 volts. Back in the early days of telecom 600 ohms was the standard termination impedance, hence the dBu. Most pro audio gear runs at +4 dBu. What does that mean? 0 dBu is 0.77 volts so +4 dBu would be 4 dB greater, or about 1.22 volts. To go from dB to volts the formula is 10^(dB/20).

Consumer audio gear usually runs at -10dBV, or roughly 0.32 volts.

When recording your goal is to get your signal level near the nominal signal level of the equipment being used. This ensures the best S/N ratio. Many recording consoles use VU meters which are calibrated such that "0 dB" is +4 dBu. The goal is to get your signal level around 0 dB.

Well-designed gear has some amount of "headroom". Headroom is the difference between the maximum signal level and the nominal signal level. For example, the Axe-Fx II has a maximum signal level of +18 dBu. If operating at +4 dBu nominal this gives 14 dB of headroom which means that any signal peaks can be over four times higher.

In digital gear we encounter the dBFS, which is dB relative to full-scale. Full-scale is a term that indicates the maximum signal level into or out of an A/D or D/A converter, respectively. With digital converters the best performance is achieved by operating the converter such that the nominal signal level is close to full-scale. The exact voltage is unknown and irrelevant. Most digital gear will have indicators that measure the levels relative to the converter's full-scale value. For example, the input meters on the Axe-Fx indicate the input signal relative to the A/D converter's full-scale value. The "tickle the red" advice aims to operate the A/D converter near its full-scale value as the red LEDs light at 6 dB below full-scale, or -6 dBFS.

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Difficult to understand, yes. But not NEARLY as difficult to understand as how an incredibly busy gear designer finds the time and inclination to write a remedial Audio tutorial for his gear's users... instead of just saying "google it".

Very impressed.

Really like this little gems !
Thanks Cliff , this is very very appreciated !
My english is not as good as Paulasbell , but I feel the same ... VERY IMPRESSED !

No doubt about my happiness and will about sharing how great Fas , the Axe and this community are !

Well done
You deserve always more than 5 stars

Thanks Cliff !!

A good succinct article!

Excellent tutorial. Thank you very much.

I see and would agree (its like the colloquialism around here, when giving someone advice they say "correct", it sounds funny to me but, they simply are in agreement).

For example, human vision is logarithmic. We perceive light such that the light must double for it to appear twice as bright.

I agree that we perceive vision on a logarithmic scale, but if you double the light and it appears twice as bright, isn't that linear?

I agree that we perceive vision on a logarithmic scale, but if you double the light and it appears twice as bright, isn't that linear?

That is the very definition of logarithmic. Say there is 100 lumens incident on your retina. If you double that to 200 lumens you perceive that as twice bright. That's a difference of 100 lumens. If you increase it to 300 lumens (a 100 lumen increase) it doesn't appear twice again as bright. You need to double it yet again.

I agree that we perceive vision on a logarithmic scale, but if you double the light and it appears twice as bright, isn't that linear?

Map it out on a graph. Double every point. You will not get a straight line but a log function.

• Guitarmandan
Since I know zero about these things (but trying to understand and learn), when the red clip light flashes on the AXE, does that mean I hit the maximum level +18 dBu?

Since I know zero about these things (but trying to understand and learn), when the red clip light flashes on the AXE, does that mean I hit the maximum level +18 dBu?

Maybe. It means you've hit 0 dBFS (or very nearly so). If the Boost/Pad for that output is 0 dB then it will be +18 dBu. If the Boost/Pad is non-zero the level will be the amount of the pad lower.

The Boost/Pad can be thought of as the nominal output level. A Boost/Pad of 0 dB is a nominal output level of +4 dBu (with 14 dB of headroom). A Boost/Pad of 12 dB would be a nominal level of -8 dBu, which is roughly -10 dBV (with the same 14 dB of headroom).

AFAIK the Axe-Fx is the only device that uses the Boost/Pad paradigm. Most processors adjust the volume before the converter in the digital domain. The Axe-Fx adjusts the volume after the converter with a digitally controlled potentiometer. This allows the converter to be operating near full-scale at all times which maximizes S/N ratio and allows you to do the "unity-gain" thing. It costs a lot more to do it this way though.

That is the very definition of logarithmic. Say there is 100 lumens incident on your retina. If you double that to 200 lumens you perceive that as twice bright. That's a difference of 100 lumens. If you increase it to 300 lumens (a 100 lumen increase) it doesn't appear twice again as bright. You need to double it yet again.

I guess you have to continue further up the scale to make a clear distinction. If you only double it once and it is twice as bright, I guess it could be linear or logarithmic until you double it again to see what happens. Thanks.

Thank you Cliff!! Much appreciated!!!

I agree that we perceive vision on a logarithmic scale, but if you double the light and it appears twice as bright, isn't that linear?
Gotta agree with Gizmo on this one. It's a good article on a tough-to-summarize subject, but the example presented describes a linear relationship between light output and perceived brightness, as in "double the light equals double the perceived brightness."

It's like our hearing, which is also logarithmic. Doubling the audio power only results in an incremental increase in perceived volume, not a doubling of perceived volume. It takes around ten times the power to sound "twice as loud."

Still a great article on a subject that defies succinct explanation.

• touch33 and nebbi
Pitch perception is also logarithmic. 220Hz = A. 440Hz = the octave of this A, 880Hz = the next octave, not 660Hz. The former is logarithmic, the latter is linear.

Decibels describe the way we perceive audio. If we go back to the real world, the decibel describes ratios in sound pressure level (or sound power, sound intensity.... lets' not get into it too much). Since there can never be 0 air pressure (because sound wouldn't travel in a vacuum), a scale that starts with a 0 pascal measurement doesn't make sense. Instead, we use atmospheric pressure and the fluctuations due to sound traveling are measured against this.

60dB SPL = 0.02 Pa.
80dB SPL = 0.2 Pa. (A jump of .18 Pa)
100dB SPL = 2 Pa. (A jump of 19.8 Pa.... a huge increase in values that corresponds to only a 20 dBSPL jump, which is far more manageable in calculations, and corresponds to how our ears perceive sound.)

Note, these values, and their corresponding real-world jumps do NOT hold true for all decibel types (hence, so many different types) but the principle remains the same.

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We are logaritmic animals... Thanks Cliff, as a sound engineer I think to know this subject but it's always a pleasure when somebody (like you) takes time to explain them again • PacoCasanovasOld and Noriuky73
Cliff can you please explain why some level meters show a doubled signal as a 3dB increase and use 10*Log(dB2/dB1) but others like SPL Meters show a 6dB increase and use 20*Log(dB2/dB1) and some references say our ears need a 10dB increase to hear a doubled signal but I couldn't find an equation for the ear? I've read a lot of info about this on www.sengpielaudio.com/Searchengine.htm (Do a search for dB and SPL) so I understand what all the different dB measurements reference but I'm still confused how some things say a doubled signal will be 3dB, 6dB or 10dB and why they don't all reference the same thing.

What does the Axe-Fx II use for the level meters? How many dB would I have to increase to sound like I added a 2nd guitarist?

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Gotta agree with Gizmo on this one. It's a good article on a tough-to-summarize subject, but the example presented describes a linear relationship between light output and perceived brightness, as in "double the light equals double the perceived brightness."

It's like our hearing, which is also logarithmic. Doubling the audio power only results in an incremental increase in perceived volume, not a doubling of perceived volume. It takes around ten times the power to sound "twice as loud."

Still a great article on a subject that defies succinct explanation.

The light example is a little more abstract in a sense.

It is exponential, but in base 2, not base 10. In base two exponential growth is a linear doubling in base 10.